- Eric Weisstein's World of Mathematics is an online math encyclopedia with many entries related to number theory.
- Wikipedia, the free encyclopedia, has a lot of information on Number theory and much else besides. See this entry, or this one, for example.
- The Number theory section of the Mathematical Atlas gives an overview of the subject of number theory.
- Chris Caldwell's Prime Pages contain a great deal of useful, interesting and occasionally silly information about prime numbers. For example, here's some information about some (possibly) illegal prime numbers.
- The Great Internet Mersenne Prime Search (GIMPS) is a distributed computing project searching for ever larger Mersenne primes.
- PRIMO is a primality proving program by Marcel Martin, based on the elliptic curve primality proving algorithm. It can be found here, along with information about the largest numbers that were proved prime using a general-purpose primality proving algorithm.
- FactorWorld is a web site dedicated to integer factorization results and algorithms. It includes a list of recent factoring records.
- RSA Security Inc. Public-Key Cryptography Standards (PKCS) includes recommendations for practical implementations of the RSA cryptosystem. These might give you some idea of the gap between the simple mathematical model of RSA given in class and a real-world implementation.
- The Online Encyclopedia of Integer Sequences is a gigantic searchable database of integer sequences. Try looking up the sequence 2,3,7,43,... for example.
- Python is a free, general-purpose programming language that's very useful for doing basic number theory calculations, thanks to its interactive interpreter and its unbounded integers. (I often use it to double-check solutions to numeric homework problems.)
- Pari-GP is a free (as in beer and speech) calculator for number theory.
- GMP is a library of routines for arbitrary precision arithmetic. The homepage includes a very useful online calculator.
- The Math Puzzle site is a great place to look for recreational mathematics, and has much that's related to number theory. For example: what's special about the decimal expansion of 1/999998999999? Find the answer, courtesy of Richard Guy, somewhere on this page.
- The Number Theory Web pages at Vancouver contain many number theory-related links and resources.
- Here's some information on Sun Zi and the Chinese Remainder Theorem, part of a History of Mathematics site at Simon Fraser University.
- Biographies of mathematicians from Pythagoras and Sun Zi through to Andrew Wiles can be found at The MacTutor History of Mathematics archive at the University of St. Andrews, Scotland.
- The Most Common Errors in Undergraduate Mathematics makes interesting reading, but the sections on Errors in Communication and Errors in Reasoning ought to be required reading for this course! See especially the section on working backwards.